question_answer 56)

Consider a binary operation * on N defined as a * b = a3 + b3, Choose the correct answer. (a) Is * both associative and commutative ? (b) Is * commutative and not associative ? (c) Is * associative but not commutative ? (d) Is * neither commutative nor associative ?  

Answer:

Let a, b and c be three element of N                        commutative.       Also (a * b) * c = (a2 + b3) * c                     = (a3 + b3)3 + c3       and a * (b * c) = a* (b2 + c3)             = a3 + (b3 + c3)3        (a *b) *        not associative  is correct.